6n(2n-8)=24-6n

Solution for 6n(2n-8)=24-6n equation:

6n(2n-8)=24-6n

We move all terms to the left:

6n(2n-8)-(24-6n)=0

We add all the numbers together, and all the variables

6n(2n-8)-(-6n+24)=0

We multiply parentheses

12n^2-48n-(-6n+24)=0

We get rid of parentheses

12n^2-48n+6n-24=0

We add all the numbers together, and all the variables

12n^2-42n-24=0

a = 12; b = -42; c = -24;
Δ = b2-4ac
Δ = -422-4·12·(-24)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-54}{2*12}=\frac{-12}{24}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+54}{2*12}=\frac{96}{24}
=4
$